Despite sustained Leicester pressure and raucous support from the City faithful inside the King Power Stadium, Atletico held on to complete a 2-1 aggregate win.
Leicester had hoped to become the competition's first debutant semi-finalists since Villarreal in 2006. But they were unable repeat their last-16 triumph against Sevilla. Leicester's exit ends an adventure sparked by last season's Premier League title win.
Leicester's desire to make the most of the occasion was clear from the start. Pyrotechnic bursts greeted the players as they emerged from the tunnel while fans twirled blue, white and gold foil flags distributed by the club.
But whereas Leicester had quickly taken charge of their second-leg match against Sevilla in the last 16, Atletico showed they were made of sterner stuff. They defended with their customary fortitude while two dangerous crosses from Yannick Carrasco demonstrated their threat on the counter-attack.
It was just as Leicester were threatening to make inroads - Shinji Okazaki stabbing wide at the near post from Vardy's cross - that the visitors tightened their grip on the tie.
Filipe Luis crossed the ball into the penalty area from the left and the unmarked Saul guided a header past City goalkeeper Kasper Schmeichel.
Shakespeare switched to a bold 3-4-3 system for the second half with Ben Chilwell and Leonardo Ulloa replacing Yohan Benalouane and Okazaki. And the shift brought results. After Chilwell had thrashed the ball over the bar, Leicester levelled. Vardy slammed home from inside the six-yard box after Chilwell's shot had been blocked.
With City requiring two more goals to advance, the final half-hour was one-way traffic. But Atletico's defensive wall was not breached.
Leicester City manager Craig Shakespeare said after the tie: "The players are very disappointed to be out of the competition but they can be proud of what they've achieved and we can be proud of how we've conducted ourselves. The players should want more of this."
With City in mid table in the English Premier League after a flirtation with relegation to the second division, competing in European club football's most prestigious tournament willnot be available until at least the 2018/19 season.
Shakespeare added: "All players want to play at the highest level and the Champions League is the highest level. We have to get back to winning ways in the Premier League now."